$K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 5x - 2$ and $ KL = 2x + 19$ Find $JL$.
A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {5x - 2} = {2x + 19}$ Solve for $x$ $ 3x = 21$ $ x = 7$ Substitute $7$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 5({7}) - 2$ $ KL = 2({7}) + 19$ $ JK = 35 - 2$ $ KL = 14 + 19$ $ JK = 33$ $ KL = 33$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {33} + {33}$ $ JL = 66$